Each individual radioactive substance has a characteristic decay period or half-life. A half-life is the interval of time required for one-half of the atomic nuclei of a radioactive sample to decay. The radioactive isotope cobalt 60, which is used in radiation cancer therapy, has, for example, a half-life of 5. Thus after that interval, a sample originally containing 16 grams of cobalt 60 would contain only 8 grams of cobalt 60 and would emit only half as much radiation.
Austin State University with contributing authors. Elizabeth R. Gordon Furman University. Learning Objectives Define half-life. Determine the amount of radioactive substance remaining after a given number of half-lives. Define a radioactive decay series. Solution If we compare the time that has passed to the isotope's half-life, we note that Answer 0. Answer 10 days. Uranium Decay Series The naturally occurring radioactive isotopes of the heaviest elements fall into chains of successive disintegrations, or decays, and all the species in one chain constitute a radioactive family, or radioactive decay series.
Radioactive Dating Radioactive dating is a process by which the approximate age of an object is determined through the use of certain radioactive nuclides. After death, the C decays and the CC ratio in the remains decreases. Comparing this ratio to the CC ratio in living organisms allows us to determine how long ago the organism lived and died. CC-BY 4. Solution Go to Link below for more details www.
Radioactive Dating Using Nuclides Other than Carbon Radioactive dating can also use other radioactive nuclides with longer half-lives to date older events. Summary Natural radioactive processes are characterized by a half-life, the time it takes for half of the material to decay radioactively. Its half-life is approximately years.
Such nuclei lie above the band of stability. Emission of an electron does not change the mass number of the nuclide but does increase the number of its protons and decrease the number of its neutrons. Consequently, the n:p ratio is decreased, and the daughter nuclide lies closer to the band of stability than did the parent nuclide. Oxygen is an example of a nuclide that undergoes positron emission:. Positron emission is observed for nuclides in which the n:p ratio is low.
These nuclides lie below the band of stability. Positron decay is the conversion of a proton into a neutron with the emission of a positron. The n:p ratio increases, and the daughter nuclide lies closer to the band of stability than did the parent nuclide. For example, potassium undergoes electron capture:.
Electron capture occurs when an inner shell electron combines with a proton and is converted into a neutron. The loss of an inner shell electron leaves a vacancy that will be filled by one of the outer electrons. As the outer electron drops into the vacancy, it will emit energy. In most cases, the energy emitted will be in the form of an X-ray.
Electron capture has the same effect on the nucleus as does positron emission: The atomic number is decreased by one and the mass number does not change. This increases the n:p ratio, and the daughter nuclide lies closer to the band of stability than did the parent nuclide. Whether electron capture or positron emission occurs is difficult to predict.
The choice is primarily due to kinetic factors, with the one requiring the smaller activation energy being the one more likely to occur. Figure 3 summarizes these types of decay, along with their equations and changes in atomic and mass numbers. To perform a PET scan, a positron-emitting radioisotope is produced in a cyclotron and then attached to a substance that is used by the part of the body being investigated.
How FDG is used by the body provides critical diagnostic information; for example, since cancers use glucose differently than normal tissues, FDG can reveal cancers. The 18 F emits positrons that interact with nearby electrons, producing a burst of gamma radiation. Different levels of gamma radiation produce different amounts of brightness and colors in the image, which can then be interpreted by a radiologist to reveal what is going on.
Unlike magnetic resonance imaging and X-rays, which only show how something looks, the big advantage of PET scans is that they show how something functions. PET scans are now usually performed in conjunction with a computed tomography scan. The naturally occurring radioactive isotopes of the heaviest elements fall into chains of successive disintegrations, or decays, and all the species in one chain constitute a radioactive family, or radioactive decay series.
Three of these series include most of the naturally radioactive elements of the periodic table. They are the uranium series, the actinide series, and the thorium series. The neptunium series is a fourth series, which is no longer significant on the earth because of the short half-lives of the species involved.
Each series is characterized by a parent first member that has a long half-life and a series of daughter nuclides that ultimately lead to a stable end-product—that is, a nuclide on the band of stability Figure 5. In all three series, the end-product is a stable isotope of lead. The neptunium series, previously thought to terminate with bismuth, terminates with thallium Radioactive decay follows first-order kinetics.
Since first-order reactions have already been covered in detail in the kinetics chapter, we will now apply those concepts to nuclear decay reactions. For example, cobalt, an isotope that emits gamma rays used to treat cancer, has a half-life of 5. Note that for a given substance, the intensity of radiation that it produces is directly proportional to the rate of decay of the substance and the amount of the substance.
This is as expected for a process following first-order kinetics. Thus, a cobalt source that is used for cancer treatment must be replaced regularly to continue to be effective. Enrico Fermi was nearly unique among 20th-century physicists—he made significant contributions both as an experimentalist and a theorist.
His many contributions to theoretical physics included the identification of the weak nuclear force. The fermi fm is named after him, as are an entire class of subatomic particles fermions , an element Fermium , and a major research laboratory Fermilab. His experimental work included studies of radioactivity, for which he won the Nobel Prize in physics, and creation of the first nuclear chain reaction.
The neutrino also reveals a new conservation law. There are various families of particles, one of which is the electron family. We propose that the number of members of the electron family is constant in any process or any closed system. In our example of beta decay, there are no members of the electron family present before the decay, but after, there is an electron and a neutrino. The bar indicates this is a particle of antimatter. All particles have antimatter counterparts that are nearly identical except that they have the opposite charge.
Antimatter is almost entirely absent on Earth, but it is found in nuclear decay and other nuclear and particle reactions as well as in outer space. The total is zero, before and after the decay. The new conservation law, obeyed in all circumstances, states that the total electron family number is constant. An electron cannot be created without also creating an antimatter family member.
This law is analogous to the conservation of charge in a situation where total charge is originally zero, and equal amounts of positive and negative charge must be created in a reaction to keep the total zero.
It is as if one of the neutrons in the parent nucleus decays into a proton, electron, and neutrino. Figure 4. The daughter nucleus has one more proton and one less neutron than its parent. Neutrinos interact so weakly that they are almost never directly observed, but they play a fundamental role in particle physics. Angular momentum is conserved, but not obviously you have to examine the spins and angular momenta of the final products in detail to verify this.
Linear momentum is also conserved, again imparting most of the decay energy to the electron and the antineutrino, since they are of low and zero mass, respectively. Another new conservation law is obeyed here and elsewhere in nature. The total number of nucleons A is conserved. In 60 Co decay, for example, there are 60 nucleons before and after the decay.
The initial mass is just that of the parent nucleus, and the final mass is that of the daughter nucleus and the electron created in the decay. The neutrino is massless, or nearly so. Beyond that are other implications. Again the decay energy is in the MeV range. This energy is shared by all of the products of the decay.
Most of the remaining energy goes to the electron and neutrino, since the recoil kinetic energy of the daughter nucleus is small. Figure 5. The second type of beta decay is less common than the first. Certain nuclides decay by the emission of a positive electron.
This is antielectron or positron decay see Figure 5. Antielectrons are the antimatter counterpart to electrons, being nearly identical, having the same mass, spin, and so on, but having a positive charge and an electron family number of —1.
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